Experimental set up

A compound channel setup was used for this case study. The paper including all information about the experience was found in Dupuis et al. (2017).

Objectives and remarks of the case study

Calibration data

A sample was taken of all measurements for this case.

event reach x t WSE Discharge Velocity Y_Kmin Y_Kmoy Yu_z Yu_Q Yu_V Yu_Kmin Yu_Kmoy
1 1 2.225 3420 0.1949608 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 4.310 3420 0.1880788 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 5.270 3420 0.1852095 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 6.240 3420 0.1829345 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 8.315 3420 0.1767361 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 9.115 3420 0.1744950 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 9.250 3420 0.1744835 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 10.250 3420 0.1737731 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 11.250 3420 0.1732561 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 12.250 3420 0.1728932 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 13.250 3420 0.1729610 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 2.225 3420 0.1902885 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 2.975 3420 0.1911852 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 3.345 3420 0.1892610 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 4.095 3420 0.1882043 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 5.060 3420 0.1864261 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 6.240 3420 0.1797323 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 6.990 3420 0.1818093 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 8.030 3420 0.1790497 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 8.795 3420 0.1743624 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.065 3420 0.1760431 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.115 3420 0.1721755 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.545 3420 0.1748087 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 10.030 3420 0.1738211 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 11.370 3420 0.1701349 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 12.120 3420 0.1723571 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 12.325 3420 0.1718688 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 13.290 3420 0.1715232 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999

Estimation: constant in the main channel and the floodplain (n_kmin = 0 and n_kflood = 2)

Check MCMC

Partial conclusions:

MCMC unstabilities are observed for all the parameters. Non convergence has been atteint during the estimation.

Check summary

Zoom into the MAP and standard deviation of the error model: WSE in mm, discharge in L/s and velocity in mm/s.
a0_min a0_flood a1_flood a2_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
N 5.62600e+03 5626.00000 5626.00000 5626.00000 5.62600e+03 5626.000000 5626.000000 5626.000000 5626.000000
Minimum 3.55184e+01 0.23387 -1649.16000 -361.31500 5.00000e-07 5.409260 4.733140 4.586530 4.809350
Maximum 3.80910e+03 1316.18000 529.62900 726.81500 1.90994e-02 21.342000 19.417600 26.271400 19.035800
Range 3.77358e+03 1315.95000 2178.79000 1088.13000 1.90989e-02 15.932700 14.684500 21.684900 14.226400
Mean 3.80925e+02 215.93000 -74.06050 59.93410 3.64720e-03 10.200500 10.197200 10.006100 10.231800
Median 8.95089e+01 144.77400 1.12262 5.65817 3.02540e-03 9.996930 9.997970 9.834780 10.058500
Q10% 5.52200e+01 26.66660 -693.56600 -85.22800 6.35200e-04 7.735390 7.683250 7.567800 7.731010
Q25% 6.64882e+01 63.29960 -19.95560 -6.18817 1.55030e-03 8.795520 8.674330 8.630330 8.776950
Q75% 2.00965e+02 263.03100 117.53100 89.93690 5.09150e-03 11.421300 11.455500 11.210800 11.522900
Q90% 1.48642e+03 499.93300 331.60000 299.15600 7.51320e-03 12.853500 13.116400 12.572400 12.881300
St.Dev. 6.77711e+02 232.48200 395.88900 172.34800 2.75550e-03 2.028350 2.146470 2.064640 2.015110
Variance 4.59292e+05 54047.90000 156728.00000 29703.90000 7.60000e-06 4.114190 4.607330 4.262730 4.060650
CV 1.77912e+00 1.07665 5.34548 2.87563 7.55499e-01 0.198848 0.210495 0.206337 0.196945
Skewness 2.45334e+00 2.04403 -1.71270 1.17837 1.13990e+00 0.696739 0.655586 0.852583 0.556058
Kurtosis 5.13545e+00 4.22783 2.76191 2.19167 1.44975e+00 1.163800 0.541119 2.926970 0.319571
MaxPost 1.64516e+02 9.47946 5.31925 5.32603 1.80120e-03 9.848100 9.865230 9.204450 9.287330
a0_min a0_flood a1_flood a2_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
St.Dev. 677.711 232.48200 395.88900 172.34800 2.75547 2028.35 214.647 2.06464 2.01511
MaxPost 164.516 9.47946 5.31925 5.32603 1.80125 9848.10 986.523 9.20445 9.28733

Check spatial friction distribution

Partial conclusions:

  • The estimated values are not coherent.

Check of residuals

event reach x t WSE Discharge Velocity Y_Kmin Y_Kmoy Yu_z Yu_Q Yu_V Yu_Kmin Yu_Kmoy
1 1 2.225 3420 0.1949608 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 4.310 3420 0.1880788 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 5.270 3420 0.1852095 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 6.240 3420 0.1829345 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 8.315 3420 0.1767361 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 9.115 3420 0.1744950 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 9.250 3420 0.1744835 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 10.250 3420 0.1737731 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 11.250 3420 0.1732561 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 12.250 3420 0.1728932 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 13.250 3420 0.1729610 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 2.225 3420 0.1902885 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 2.975 3420 0.1911852 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 3.345 3420 0.1892610 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 4.095 3420 0.1882043 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 5.060 3420 0.1864261 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 6.240 3420 0.1797323 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 6.990 3420 0.1818093 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 8.030 3420 0.1790497 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 8.795 3420 0.1743624 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.065 3420 0.1760431 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.115 3420 0.1721755 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.545 3420 0.1748087 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 10.030 3420 0.1738211 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 11.370 3420 0.1701349 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 12.120 3420 0.1723571 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 12.325 3420 0.1718688 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 13.290 3420 0.1715232 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999

Partial conclusions:

All simulations of MAP estimation are passing through the observed data with their uncertainty.

Estimation (n_kmin = 0 and n_kflood = 2, with lower uncertainty)

Check MCMC

Partial conclusions:

Check summary

Zoom into the MAP and standard deviation of the error model: WSE in mm, discharge in L/s and velocity in mm/s.
a0_min a0_flood a1_flood a2_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
N 5.62600e+03 5626.000000 5626.000000 5626.0000000 5.62600e+03 5626.000000 5626.000000 5626.000000 5626.000000
Minimum 6.75107e+01 6.469160 -906.062000 -0.7573170 2.20000e-06 4.691900 5.153310 4.907100 5.132820
Maximum 3.76359e+03 623.575000 3.415800 445.0820000 8.49710e-03 19.618200 22.568900 19.288500 19.072600
Range 3.69608e+03 617.106000 909.478000 445.8390000 8.49490e-03 14.926300 17.415600 14.381400 13.939800
Mean 7.08821e+02 184.403000 -254.284000 112.8090000 1.45270e-03 10.241000 10.269800 10.210000 10.273000
Median 4.43296e+02 127.911000 -184.112000 91.1873000 1.14500e-03 10.045800 10.006700 10.031300 10.114900
Q10% 1.13531e+02 30.370700 -592.779000 10.0411000 2.22500e-04 7.826580 7.763490 7.726840 7.853240
Q25% 1.43163e+02 53.332800 -449.539000 24.8515000 5.47400e-04 8.830190 8.689880 8.720070 8.844560
Q75% 1.09482e+03 299.779000 -22.523900 184.4360000 2.12150e-03 11.473300 11.474700 11.395800 11.502200
Q90% 1.77611e+03 407.080000 -9.443910 238.5600000 3.06040e-03 12.887600 13.060000 13.022800 12.874700
St.Dev. 6.92355e+02 145.974000 239.004000 94.9262000 1.16140e-03 2.048740 2.193510 2.120600 2.023380
Variance 4.79356e+05 21308.300000 57123.100000 9010.9800000 1.30000e-06 4.197320 4.811480 4.496930 4.094050
CV 9.76770e-01 0.791603 0.939910 0.8414740 7.99460e-01 0.200052 0.213588 0.207697 0.196961
Skewness 1.20876e+00 0.677851 -0.617061 0.7780830 1.22652e+00 0.590819 0.874968 0.665839 0.605191
Kurtosis 8.19305e-01 -0.728789 -0.798636 -0.0533204 1.91539e+00 0.533511 1.382410 0.667490 0.521433
MaxPost 1.30432e+02 31.930300 -10.834200 22.9262000 3.75100e-04 9.156150 9.644310 9.403030 10.409300
a0_min a0_flood a1_flood a2_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
St.Dev. 692.355 145.9740 239.0040 94.9262 1.161410 2048.74 219.351 2.12060 2.02338
MaxPost 130.432 31.9303 -10.8342 22.9262 0.375124 9156.15 964.431 9.40303 10.40930

Check spatial friction distribution

Partial conclusions:

Check of residuals

event reach x t WSE Discharge Velocity Y_Kmin Y_Kmoy Yu_z Yu_Q Yu_V Yu_Kmin Yu_Kmoy
1 1 2.225 3420 0.1949608 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 4.310 3420 0.1880788 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 5.270 3420 0.1852095 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 6.240 3420 0.1829345 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 8.315 3420 0.1767361 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 9.115 3420 0.1744950 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 9.250 3420 0.1744835 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 10.250 3420 0.1737731 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 11.250 3420 0.1732561 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 12.250 3420 0.1728932 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 13.250 3420 0.1729610 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 2.225 3420 0.1902885 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 2.975 3420 0.1911852 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 3.345 3420 0.1892610 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 4.095 3420 0.1882043 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 5.060 3420 0.1864261 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 6.240 3420 0.1797323 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 6.990 3420 0.1818093 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 8.030 3420 0.1790497 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 8.795 3420 0.1743624 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 9.065 3420 0.1760431 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 9.115 3420 0.1721755 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 9.545 3420 0.1748087 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 10.030 3420 0.1738211 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 11.370 3420 0.1701349 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 12.120 3420 0.1723571 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 12.325 3420 0.1718688 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 13.290 3420 0.1715232 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999

Partial conclusions:

Estimation (n_kmin = 0 and n_kflood = 4)

Check MCMC

Partial conclusions:

Check summary

Zoom into the MAP and standard deviation of the error model: WSE in mm, discharge in L/s and velocity in mm/s.
a0_min a0_flood a1_flood a2_flood a3_flood a4_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
N 5626.00000 5626.000000 5626.000000 5626.000000 5626.000000 5.62600e+03 5.62600e+03 5626.000000 5626.000000 5626.000000 5.62600e+03
Minimum 34.08810 0.149982 -714.229000 -876.929000 -1115.750000 -1.13655e+03 6.40000e-06 5.188060 4.875490 4.787370 4.66734e+00
Maximum 1595.27000 329.581000 509.053000 1014.560000 816.162000 5.64543e+02 2.15719e-02 19.807000 20.685000 20.019600 1.98484e+01
Range 1561.18000 329.431000 1223.280000 1891.490000 1931.910000 1.70109e+03 2.15655e-02 14.618900 15.809500 15.232200 1.51811e+01
Mean 175.29700 111.279000 -50.114700 -60.414800 45.204000 -2.23995e+02 3.63140e-03 10.297300 10.188900 10.109100 1.01979e+01
Median 89.50410 97.248900 -19.822600 0.853679 25.665100 -1.41474e+02 3.02560e-03 10.109100 9.968710 9.925880 1.00470e+01
Q10% 62.75600 18.091100 -240.079000 -374.045000 -137.345000 -6.56785e+02 5.69800e-04 7.858830 7.866260 7.645040 7.61636e+00
Q25% 71.81740 46.431600 -87.710600 -93.929900 0.527044 -3.93629e+02 1.45400e-03 8.847970 8.764370 8.636070 8.63273e+00
Q75% 159.00300 173.235000 -1.037850 19.015900 145.817000 -1.45462e+01 5.18570e-03 11.494700 11.417100 11.365800 1.15893e+01
Q90% 417.13300 219.720000 115.779000 44.899300 325.875000 -4.82369e-01 7.55810e-03 12.979000 12.883400 12.771200 1.30527e+01
St.Dev. 218.22500 75.380200 155.191000 216.661000 262.940000 2.74926e+02 2.79570e-03 2.040720 2.027860 2.053500 2.07258e+00
Variance 47622.10000 5682.170000 24084.300000 46942.100000 69137.700000 7.55842e+04 7.80000e-06 4.164530 4.112220 4.216860 4.29559e+00
CV 1.24488 0.677396 3.096720 3.586230 5.816750 1.22737e+00 7.69879e-01 0.198180 0.199027 0.203133 2.03236e-01
Skewness 2.94893 0.436424 -0.574716 -0.441637 -1.354490 -6.06785e-01 1.13053e+00 0.571616 0.624735 0.576387 4.21090e-01
Kurtosis 9.09418 -0.794598 2.669210 4.755250 4.643280 7.06489e-02 1.62841e+00 0.643217 0.804943 0.626208 8.73986e-02
MaxPost 250.65500 2.591520 2.466420 0.405612 2.052370 -3.72801e+00 1.48080e-03 9.550830 9.965600 10.677200 9.51736e+00
a0_min a0_flood a1_flood a2_flood a3_flood a4_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
St.Dev. 218.225 75.38020 155.19100 216.661000 262.94000 274.92600 2.79574 2040.72 202.786 2.0535 2.07258
MaxPost 250.655 2.59152 2.46642 0.405612 2.05237 -3.72801 1.48076 9550.83 996.560 10.6772 9.51736

Check spatial friction distribution

Partial conclusions:

Check of residuals

event reach x t WSE Discharge Velocity Y_Kmin Y_Kmoy Yu_z Yu_Q Yu_V Yu_Kmin Yu_Kmoy
1 1 2.225 3420 0.1949608 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 4.310 3420 0.1880788 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 5.270 3420 0.1852095 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 6.240 3420 0.1829345 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 8.315 3420 0.1767361 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 9.115 3420 0.1744950 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 9.250 3420 0.1744835 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 10.250 3420 0.1737731 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 11.250 3420 0.1732561 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 12.250 3420 0.1728932 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
1 1 13.250 3420 0.1729610 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 2.225 3420 0.1902885 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 2.975 3420 0.1911852 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 3.345 3420 0.1892610 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 4.095 3420 0.1882043 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 5.060 3420 0.1864261 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 6.240 3420 0.1797323 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 6.990 3420 0.1818093 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 8.030 3420 0.1790497 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 8.795 3420 0.1743624 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.065 3420 0.1760431 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.115 3420 0.1721755 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 9.545 3420 0.1748087 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 10.030 3420 0.1738211 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 11.370 3420 0.1701349 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 12.120 3420 0.1723571 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 12.325 3420 0.1718688 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999
2 1 13.290 3420 0.1715232 -9999 -9999 -9999 -9999 0.0222257 -9999 -9999 -9999 -9999

Estimation (n_kmin = 0 and n_kflood = 4, with lower uncertainty)

Check MCMC

Partial conclusions:

Check summary

Zoom into the MAP and standard deviation of the error model: WSE in mm, discharge in L/s and velocity in mm/s.
a0_min a0_flood a1_flood a2_flood a3_flood a4_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
N 5626.000000 5626.000000 5.62600e+03 5626.000000 5626.00000 5626.000000 5.62600e+03 5626.000000 5626.000000 5626.000000 5626.000000
Minimum 45.384900 0.645952 -1.12552e+02 -820.216000 -711.74200 -996.927000 1.10000e-06 5.251240 5.355910 4.872830 4.401990
Maximum 269.872000 338.195000 6.88412e+02 398.163000 665.78300 719.385000 6.56170e-03 20.015800 21.821500 22.341300 18.295500
Range 224.487000 337.549000 8.00964e+02 1218.380000 1377.53000 1716.310000 6.56070e-03 14.764600 16.465600 17.468500 13.893500
Mean 101.143000 100.198000 1.07237e+02 73.911700 -60.51250 24.161000 1.38490e-03 10.197400 10.253100 10.291300 10.179400
Median 76.734600 70.955500 1.63633e+00 34.127000 1.29157 -0.556933 1.12060e-03 10.064100 10.061700 10.078900 10.010700
Q10% 58.998400 13.520600 -4.93987e+01 -30.213800 -342.17100 -93.134000 2.24300e-04 7.784890 7.762610 7.793300 7.639570
Q25% 66.375400 28.300500 -2.37196e+01 7.815460 -147.22500 -26.030400 5.03100e-04 8.733890 8.732530 8.860140 8.678860
Q75% 140.167000 160.082000 2.09499e+02 170.057000 22.65480 67.397200 2.01190e-03 11.431000 11.502300 11.531100 11.490200
Q90% 175.526000 240.423000 4.19283e+02 262.329000 105.22600 189.517000 3.04640e-03 12.837100 12.972500 13.068300 12.990700
St.Dev. 47.770500 85.409700 1.83531e+02 131.113000 176.85200 154.292000 1.10360e-03 2.023590 2.098270 2.054680 2.089490
Variance 2282.020000 7294.820000 3.36837e+04 17190.700000 31276.60000 23806.000000 1.20000e-06 4.094930 4.402740 4.221700 4.365960
CV 0.472307 0.852407 1.71145e+00 1.773920 2.92257 6.385980 7.96907e-01 0.198441 0.204647 0.199652 0.205266
Skewness 1.049390 0.806604 1.10736e+00 -0.576183 -1.03814 -0.184789 1.10553e+00 0.595984 0.697967 0.561048 0.507925
Kurtosis -0.099795 -0.542128 -3.90113e-02 3.452190 1.09225 9.423940 1.12833e+00 0.706034 0.994271 0.525864 0.260188
MaxPost 188.472000 31.866300 -3.01994e+01 26.820700 -5.81556 1.553310 2.54800e-04 8.733280 9.245970 9.449770 10.113700
a0_min a0_flood a1_flood a2_flood a3_flood a4_flood Y1_intercept Y2_intercept Y3_intercept Y4_intercept Y5_intercept
St.Dev. 47.7705 85.4097 183.5310 131.1130 176.85200 154.29200 1.103620 2023.59 209.827 2.05468 2.08949
MaxPost 188.4720 31.8663 -30.1994 26.8207 -5.81556 1.55331 0.254818 8733.28 924.597 9.44977 10.11370

Check spatial friction distribution

Partial conclusions:

Check of residuals

event reach x t WSE Discharge Velocity Y_Kmin Y_Kmoy Yu_z Yu_Q Yu_V Yu_Kmin Yu_Kmoy
1 1 2.225 3420 0.1949608 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 4.310 3420 0.1880788 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 5.270 3420 0.1852095 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 6.240 3420 0.1829345 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 8.315 3420 0.1767361 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 9.115 3420 0.1744950 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 9.250 3420 0.1744835 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 10.250 3420 0.1737731 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 11.250 3420 0.1732561 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 12.250 3420 0.1728932 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
1 1 13.250 3420 0.1729610 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 2.225 3420 0.1902885 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 2.975 3420 0.1911852 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 3.345 3420 0.1892610 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 4.095 3420 0.1882043 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 5.060 3420 0.1864261 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 6.240 3420 0.1797323 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 6.990 3420 0.1818093 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 8.030 3420 0.1790497 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 8.795 3420 0.1743624 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 9.065 3420 0.1760431 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 9.115 3420 0.1721755 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 9.545 3420 0.1748087 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 10.030 3420 0.1738211 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 11.370 3420 0.1701349 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 12.120 3420 0.1723571 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 12.325 3420 0.1718688 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999
2 1 13.290 3420 0.1715232 -9999 -9999 -9999 -9999 0.008 -9999 -9999 -9999 -9999

Main conclusions:

  • Thee streamwise distance as covariant to spatial distribute the friction coefficient is not enough to estimate the friction coefficient when the roughness changes suddenly. Changes are modelized smoothly, but the real-world conditions are not.
  • However, this example allows to prove that the methodology is able to estimate constant friction using a picewise function (to be tested)

Bibliography:

Dupuis, Victor, Sébastien Proust, Céline Berni, and André Paquier. 2017. “Compound Channel Flow with a Longitudinal Transition in Hydraulic Roughness over the Floodplains.” Environmental Fluid Mechanics 17 (5): 903–28. https://doi.org/10.1007/s10652-017-9525-0.